Question: Rewrite as a simplified fraction. ${2.86\overline{5} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2865.5555...\\ 100x &= 286.5555...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2579}$ ${x = \dfrac{2579}{900}} \text{or} {2 \dfrac{779}{900}}$